Supplemental Figures
Morgan Kain, Ben Bolker
Supplemental material for “Can existing data on WNV infection in birds and mosquitos explain strain replacement?”
(1) Description of the model converting titer in mosquito bodies to transmission probability
+ Figure S1
(2) Description of the model fitted to mosquito survival
+ Figure S2
(3) Titer and Survival for “Other” Birds + Figures S3.1–S3.2
(4) Mosquito to bird transmission adjustments
+ Figures S4.1–S4.7
(5) Results of R\(\sf{_{0}}\) calculations without using data from JEV for lower titer ranges
+ Figure S5
(6) Coefficient plots for all models
+ Titer profiles: Figures S6.1, S6.2
+ Bird Survival: Figures S6.3, S6.4
+ Bird to Mosquito Transmission: Figures S6.5, S6.6
+ Mosquito to Bird Transmission: Figures S6.7-S6.12
(7) Amplification Fraction Table
+ Table S1
(8) Stan model notes
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Section 1: Model for mosquito titer to mosquito transmission ————————————————————————————————————————————————————————
*Due to a lack of publications that explicitly measured transmission from mosquitos after X days following infection with WNV, we fit a model to transmission with titer as a predictor used data from Moudy et al. 2007 to obtain data from papers that only measured titer temporally and not transmission. To do so we fit a parameterization of a logistic cdf to transmission using non-linear least squares with the nlxb package (Nash 2014).
Figure S1: Relationship between Titer and Transmission from Moudy et al. 2007
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Section 2: Model for mosquito survival ————————————————————————————————————————————————————————
*We used data from Andreadis et al. 2014 to fit a logistic model to mosqutio longevity. In our data analysis we used median survival at each temperature to calculate R\(\sf{_{0}}\)
+ We appreciate that this study took place in Greece, far from the transmission events we are interested in, but it includes the most complete data on temperature dependent Culex survival that we could find
+ Colored solid lines are extracted data from Andreadis et al. 2014 Figure 1C. Colored dashed lines are model estimates
Figure S2: Relationship between Mosqutio Survival Probability and Days 
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Section 3: Titer and Survival for “Other” Birds ————————————————————————————————————————————————————————
Figure S3.1: Titer Profiles for all other birds. 
Figure S3.2: Survival for all other birds. 
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Section 4: Mosquito to bird transmission adjustments ————————————————————————————————————————————————————————
Figure S4.1: 3d figure of Mosquito to Bird model fit to raw data (NY99 with JEV data)
+ Red points are NY99 data, blue points are WN02 data. Surfaces are predicted probabilities of transmission from an infected mosquito to a naive bird (Z-axis) for NY99 with JEV data. X-axis is days from 1-40, y-axis is Log Dose from 2 to 8. Light green surface is fitted surface at 16 degrees Celcius, darker green surface is 20 degrees Celcius, and black surface is 24 degrees Celcius.
Figure S4.2: 3d figure of Mosquito to Bird model fit to raw data (WN02 with JEV data)
+ Red points are NY99 data, blue points are WN02 data. Surfaces are predicted probabilities of transmission from an infected mosquito to a naive bird (Z-axis) for WN02 with JEV data. X-axis is days from 1-40, y-axis is Log Dose from 2 to 8. Light green surface is fitted surface at 16 degrees Celcius, darker green surface is 20 degrees Celcius, and black surface is 24 degrees Celcius.
Figure S4.3: 3d figure of Mosquito to Bird model fit to raw data (NY99 without JEV data)
+ Red points are NY99 data, blue points are WN02 data. Surfaces are predicted probabilities of transmission from an infected mosquito to a naive bird (Z-axis) for NY99 without JEV data. X-axis is days from 1-40, y-axis is Log Dose from 2 to 8. Light green surface is fitted surface at 16 degrees Celcius, darker green surface is 20 degrees Celcius, and black surface is 24 degrees Celcius.
+ Note the increase in transmission probability with decreasing Log Dose
Figure S4.4: 3d figure of Mosquito to Bird model fit to raw data (WN02 without JEV data)
+ Red points are NY99 data, blue points are WN02 data. Surfaces are predicted probabilities of transmission from an infected mosquito to a naive bird (Z-axis) for WN02 without JEV data. X-axis is days from 1-40, y-axis is Log Dose from 2 to 8. Light green surface is fitted surface at 16 degrees Celcius, darker green surface is 20 degrees Celcius, and black surface is 24 degrees Celcius.
+ Note the increase in transmission probability with decreasing Log Dose 
Figure S4.5: Figure 4a from the main text without encorporating mosquito survival
Figure S4.6: Figure 4a, b from the main text without JEV data
+ See Section 5 for coefficient plots for mosquito to bird transmission without JEV data
*__Figure S4.7: Vector-Competence for NY99 and WN02*
+ Vector Competence at 26 Degrees Celcius, generated by combining Bird-to-Mosquito and Mosquito-to-Bird transmission (conditioning Mosquito-to-Bird transmission on all mosquitos that fed on an infected blood sample).
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Section 5: R\(\sf{_{0}}\) Caculations without Japanese Encephalitis Virus (JEV) data ————————————————————————————————————————————————————————
*Here we present the analysis presented in the primary manuscript removing all “prior information”" on mosquito transmission at lower titers using transmission of the closely realted JEV virus. + Here we present parameter estimates for the Mosquito to Bird transmission model and R\(\sf{_{0}}\) estimates with and without the JEV transmission data
Figure S5: R\(\sf{_{0}}\) Without JEV data + Panels correspond to Figure 5 in the main text
Community R\(\sf{_{0}}\)s without JEV In the Chicago, IL community “other” birds median R\(\sf{_{0}}\) for NY99 was greater than WN02, but credible intervals overlap:
NY99 at 16\(^{0}\)C, Median: 0.83, CI: 0.02-3.06;
WN02 at 16\(^{0}\)C, Median: 1.54, CI: 0.01-4.93;
NY99 at 26\(^{0}\)C, Median: 0.30, CI: 0.07-0.88;
WN02 at 26\(^{0}\)C, Median: 0.55, CI: 0.06-1.33.
In the Chicago, IL community “other” birds median R\(\sf{_{0}}\) WN02 was greater than NY99, but credible intervals also overlap:
NY99 at 16\(^{0}\)C, Median: 1.18, CI: 0.03-5.70;
WN02 at 16\(^{0}\)C, Median: 1.06, CI: 0.002-7.38;
NY99 at 26\(^{0}\)C, Median: 0.42, CI: 0.08-1.63;
WN02 at 26\(^{0}\)C, Median: 0.49, CI: 0.02-1.96.
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Section 6: Coefficient plots for all models ————————————————————————————————————————————————————————
*In this section we include all coefficient plots for the fixed effects, random effects, and for the linear predictors from one of the random effects of our choice for each model
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Titer
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Figure S6.1: Fixed Effects
Figure S6.2: Random Effects
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Survival
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* Figure S6.3: Fixed Effects
- Figure S6.4: Random Effects
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Bird to Mosquito Transmission
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* Figure S6.5: Fixed Effects
- Figure S6.6: Random Effects
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Mosquito to Bird Transmission: With JEV
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- Figures S6.7, S6.8: Fixed Effects
- Figure S6.9: Random Effects
- Mosquito to Bird Transmission: Without JEV
- Figure S6.10, S6.11: Fixed Effects
- Figure S6.12: Random Effects
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Section 7: Amplification Fraction Table ————————————————————————————————————————————————————————
## Species Lower Median Upper
## 1 American Crow 5.897167e-05 0.0002654346 0.003462375
## 2 House Sparrow 8.917860e-02 0.5514002264 0.939438128
## 3 House Finch 4.388876e-03 0.0310894843 0.222416533
## 4 American Robin 1.741246e-02 0.3913833886 0.891619716————————————————————————————————————————————————————————
Section 8: Stan model notes ————————————————————————————————————————————————————————
All stan models are available as .stan files in the online supplement and in the Github repository https://github.com/morgankain/WNV_Synthesis.git
For the titer profiles model (Titer_Profiles.stan) fixed effect parameters were given uninformative cauchy priors: intercepts were given cauchy(0, 10) priors and slopes were given cauchy(0, 2.5) priors following Gelman et al. 2008 (Bayesian Data Analysis). Variance parameters with positive constraints were given uninformative inv_gamma priors.
For the Bird_Survival.stan, Bird_to_Mosquito.stan, and Mosquito_to_Bird.stan models parameters without constraints such as intercept or slope coefficients, were given normal(0.0, 1.0E3) priors. Variance parameters with positive constraints were given gamma(1.0E-3, 1.0E-3) priors.